Table 2.

Characterization methods to determine surface roughness of carrier particles.

Characterization method		Equation	Result	Ref.
Direct method	Atomic force microscopy (AFM)	$R_{\mathrm{RMS}}=\sqrt{\frac{1}{n}\sum _{i=1}^n{y}_{i=1}^2}$	No significance between the surface roughness of composite carriers and regular carriers was observed due to the increased variability in sample morphology of the regular carrier.	8
	Scanning electron microscopy (SEM)	$R_{\mathrm{a}}=\frac{1}{l}{\int }_0^l|z(x)\times \mathrm{d}x$	Particles produced at large scale exhibited changes not only in surface roughness but also in shape at varying outlet temperatures. A decrease in surface roughness led to a lower FPF.	29
	Confocal laser scanning microscope (CLSM)	—	The obtained roughness profiles were consistent with results of SEM image analysis and showed distinct trends. In general, rough particles obtained at low outlet temperatures were spherical, whereas higher drying temperatures resulted in particles with multiple surface indentations and smoother surface. Different roughness was a result of underlying crystallization processes.	15, 82, 83
	Particle image analysis	$\text{Roughness}=\frac{\mathrm{Perimeter}}{\mathrm{ConvexPerim}}$	All crystallized particles had rougher surfaces than the commercial lactose, leading to improved drug aerosolization performance due to lower drug–carrier adhesion forces.	70
Indirect method	Colloid probe microscopy	—	Median force (F0.5) value was chosen as the best descriptor of drug–carrier adhesion force. The values for polymer coated/uncoated carriers followed a rank order of PVP coated >un-coated >EC coated lactose, which showed an opposite trend of FPF.	86, 89, 90
	Air depression sieving	—	It was considered as a simple method to evaluate drug–carrier adhesion force, based on the aspiration principle that the whole blend used in DPI was taken into account. The detailed procedure was presented by Le et al.91. Greater drug–carrier adhesion force was obtained under higher humidity, leading to decreased FPF. Kaialy et al.7 also used this method to evaluate the adhesion force between salbutamol sulphate and different lactose grades in the same size range, demonstrating that lactose particles with more elongated/irregular shape, and rougher surface were preferred to improve FPF.	7, 91

ConvexPerim, circumscribed particle perimeter;

l, length;

N, the number of data points in a topographical profile;

Perimeter, estimated particle perimeter;

R_a, the mean R_a values of several line profiles over the analyzed surface;

R_RMS, surface root mean square roughness;

y_i, the distance of asperities (i) from the center line;

Z, the deviation of all points from a plane fit to the test surface over sampling length l;

—, no equation was reported for the method.